Producing high efficiency gallium arsenide IMPATT diodes utilizing a gas injection system

ABSTRACT

The operating frequency of an IMPATT diode depends on the width of the depletion region formed during operation. The frequency of high efficiency GaAs IMPATT diodes comprising a non-uniformly doped depletion region contacted by a rectifying barrier can be more precisely fixed by forming a &#34;clump&#34; of charge at exactly the depth below the surface contacted by the rectifying barrier corresponding to the desired depletion region.

This application is a division of application Ser. No. 538,082, filedJan. 2, 1975, now U.S. Pat. No. 3,986,192, issued Oct. 12, 1976.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to semiconductor microwave diodes and, moreparticularly, to more precisely defining the operating frequency of highefficiency GaAs Schottky barrier diodes having non-uniformly dopeddepletion region.

2. Description of the Prior Art

There is considerable interest currently in solid state microwave energysources. Such sources promise to be more compact and less expensive, andto have considerably longer life than microwave tubes.

Among the most promising forms of solid state microwave sources is theimpact-avalanche transit-time (IMPATT) diode disclosed in U.S. Pat. Nos.2,899,646 and 2,899,652, which issued to W. T. Read, Jr. on Aug. 11,1959. A characteristic of such a diode is a multi-zone semiconductiveelement which, when operating, includes a depletion region comprising anavalanche region and a drift region. A rectifying barrier, such as aSchottky barrier, contacts the avalanche region. A dynamic negativeresistance is achieved by introducing an appropriate transit time toavalanching carriers in their travel across the drift region.

Early investigations have centered on increasing both the output powerand the frequency of operation of these devices. More recent studieshave concentrated on increasing the output efficiency, which, for GaAsIMPATT diodes, has typically ranged from about 10 percent to 15 percentof the input power.

It is now known that high efficiency (about 25 percent to 35 percent)GaAs IMPATT diodes may be obtained by more precisely defining theavalanche region. This is realized by forming a region of high dopinglevel, or "clump" of charge, at a particular depth below the Schottkybarrier contact, within that part of the body of the device thatnormally forms the depletion region when in operation. In thisdescription, that region is termed the active layer. The location of thecharge clump is dictated by desired operating frequency and efficiencyconsiderations.

A continuing problem, however, has involved attempts to define moreprecisely the output frequency of the device. This frequency depends onthe width of the depletion region, and is easily affected by materialparameter variations. For example, calculations have shown thatrelatively small (about 5 percent) changes in impurity content andposition of the charge clump result in unacceptably large (about 11percent) deviations in the operating frequency.

Summary of the Invention

In accordance with the invention, the frequency of a GaAs IMPATT diodeis fixed by forming a second region of high doping level, or "stopclump", at the depth below the surface corresponding to a desireddepletion depth. For example, for an 11 GHz device, this depth is 3.5μm; for a 6 GHz device, the depth is 6.5 μm. As a consequence, variationin the frequency of IMPATT diodes due to material parameter variationswithin a GaAs slice is minimized.

A preferred embodiment is directed to forming the stop clump by using agas injection valve to inject a known volume of a known concentration ofthe doping gas at a known pressure into the reaction chamber duringchemical vapor deposition epitaxial growth of the active layer.

BRIEF DESCRIPTION OF THE DRAWING

FIGS. 1A and 1B, on coordinates of doping level and distance into theactive layer as measured from a rectifying contact, are plots of idealnon-uniform doping profiles of high efficiency GaAs IMPATT diodes;

FIGS. 2A and 2B are front elevational views in cross section of a GaAsslice including a substrate and two epitaxial layers in which one of theepitaxial layers is doped in accordance with the invention;

FIG. 3 is a schematic view of a typical apparatus suitable for use inthe practice of the present invention; and

FIGS. 4A and 4B, on coordinates of doping level and distance into theactive layer as measured from the rectifying barrier contact, areexamples of doping profiles of GaAs slices fabricated in accordance withthe invention.

DETAILED DESCRIPTION OF THE INVENTION

The description that follows is given in terms of a GaAs Schottkybarrier IMPATT diode capable of operating in the microwave frequencyrange of about 6 GHz to 12 GHz. The inventive structure disclosed,however, can be employed over other frequency ranges as well.

IMPATT diodes with depletion regions having a variety of non-uniformdoping profiles have been shown to yield high efficiency microwave powersources; see Vol. 44, Journal of Applied Physics, pp. 314-324, 1973.Examples of such structures are illustrated in FIG. 1. FIG. 1A depicts atwo-step doping profile, or hi-lo modified Read profile. The hi-lodoping profile in FIG. 1A is characterized by a high doped layer N_(H)of thickness a and by a low doped layer N_(L) of thickness W_(E) -a,where W_(E) is the physical thickness of the active layer. FIG. 1Bdepicts a two-step field profile, or lo-hi-lo modified Read dopingprofile. The lo-hi-lo doping profile in FIG. 1B is characterized by ahigh doped layer N_(H), or "clump", containing charge Q at a meanposition a from the rectifying barrier and by low doped layers N_(L) andN_(L) ' on both sides of the high doped layer, where N_(L) and N_(L) 'may or may not be equal. The width of this high doped region is 2σ.

The plots show a depletion region, or space charge region, of width W,comprising an avalanche region a and a drift or transit region W-a.Depending on the operating conditions of the device, W may be equal orless than width W_(E). The increase in doping concentration at x = aserves to define the avalanche region more precisely than is possiblewith uniform doping across the depletion region, as the above referenceindicates. For optimum device properties, the width of the avalancheregion should range from about 4 percent to 16 percent of the width ofthe depletion region.

For both a hi-lo and a lo-hi-lo profile, a ranges from about 0.2 μm to1.0 μm, as measured from the surface contacted by the rectifyingbarrier. For a lo-hi-lo profile, the width 2σ of the charge clump rangesfrom about 100 Angstroms to 0.5 μm as measured at 60 percent of N_(H),assuming a Gaussian distribution.

Three parameters are important for efficient oscillations: (1) the widthof the avalanche region a, (2) the amount of doping of the drift regionN_(L) and (3) the amount of charge Q present near the surface (for ahi-lo profile, Y_(Q) = a N_(H) ; for a lo-hi-lo profile, Q ≃ 2σN_(H)).For optimum device properties, the measured value of Q should range fromabout 2 × 10¹² cm⁻² to 3.5 × 10¹² cm⁻². In order to maximize theefficiency of the device, the location of the highly doped region andthe carrier concentration in that region must be carefully controlled.As shown in the above reference, a theoretical operating efficiency forGaAs IMPATT diodes having a hi-lo profile is 33.9 percent of the inputpower, while the theoretical efficiency for a lo-hi-lo profile is 32.3percent of the input power.

The principle factor in obtaining an acceptable yield of devices withhigh efficiency performance at a specific frequency, f, is theuniformity and specific value of device space charge width W at theonset of avalanche. The variations in space charge width ΔW and indevice frequency Δf are related as ##EQU1##

Thus, the frequency f of the device depends on the width of thedepletion region, W. For a hi-lo profile, W depends on the values ofN_(H), a, and N_(L). For a lo-hi-lo profile, W depends on the values ofQ, a, and N_(L). Thus, W is sensitive to variations in these materialparameters. It should be noted that for non-uniformly doped depletionregions, W is more sensitive by at least a factor of 2 to materialparameter variations than for uniformly-doped depletion regions.Consequently, for diodes having non-uniformly doped depletion regions,both dc static properties (breakdown voltage, capacitance per unit area,etc.) and microwave properties (frequency, output power, efficiency,etc.) of the device are easily affected. However, and in accordance withthe invention, W, and thus the operating frequency f, can be fixed byplacing a clump of charge, termed here a "stop clump", at exactly thedepth below the surface corresponding to a desired depletion region (3.5μm for an 11 GHz device; 6.5 μm for a 6 GHz device).

For purposes of illustration, a hi-lo structure 20 is shown in FIG. 2Aand a lo-hi-lo structure 21 is shown in FIG. 2B. The structures compriseepitaxial films 23 and 24 sequentially deposited on a highly dopedsubstrate 22, or "contact" layer, having a carrier concentration ofabout 10¹⁸ cm⁻³ and designated n⁺⁺. A first epitaxial "buffer" layer 23,having a carrier concentration of about 4 × 10¹⁷ cm⁻³ and designated n⁺,is formed on one surface of the substrate. A second epitaxial "active"layer 24, having a carrier concentration of about 10¹⁵ cm⁻³ anddesignated n, is formed on the surface of the buffer layer, and includesthe depletion region. Details of this structure are described inProceedings of the IEEE, Vol. 59, No. 8, August, 1971, pp. 1212-1215,and thus do not form a part of this invention. An IMPATT device may befabricated, as is well-known in the art, by forming either an ohmiccontact or rectifying contact on the exposed surface 25 of the substrate22 and a rectifying barrier, such as a Schottky barrier contact, on theexposed surface 27 of the active layer 24. An ultrathin layer 28 formedduring the deposition of the active layer 24, comprises the highly dopedregion for increasing the efficiency of the device. A second ultrathinlayer 29, also formed during the deposition of the active layer,comprises the "stop clump" for better defining the operating frequencyof the device, in accordance with the invention.

While the buffer layer (or, in the absence of a buffer layer, thecontact layer) may, in principle, serve to define the depletion width Wand hence the operating frequency f, it appears that the growthtechniques presently available in the art permit better control overlocating the position of the stop clump. Apparently as a result ofdiffusion effects, control over the location of the buffer layer-activelayer boundary is more difficult to attain.

The amount of change Q_(S) most desirable in the stop clump isdetermined by (a) the maximum solubility of the dopant in the epitaxialhost material and (b) the total Q (the total change in both hi and loregions) in the remainder of the depletion region. Consistent with theseconsiderations, Q_(S) advantageously may range from about 1 × 10¹² cm⁻²to 3.5 × 10¹² cm⁻².

The width of the stop clump is constrained by two considerations. Fortoo high a value, the control over frequency is lost. The lower value islimited by practical problems relating to forming thin layers.Consistent with these considerations, the width of the stop clump mayrange from about 100 Angstroms to 0.5 μm, as measured at 60 percent ofthe maximum doping level, assuming a Gaussian distribution.

In FIG. 3, a schematic representation of apparatus 30 conveniently usedin the practice of the invention is shown. A more detailed descriptionof this system is available elsewhere; see, e.g., J. V. DiLorenzo, U.S.Pat. No. 3,762,945, issued Oct. 2, 1973, and Vol. 17, Journal of CrystalGrowth, pp. 189-206, 1972. A bubbler system 31 includes a reservoir ofarsenic trichloride 32 and conduit means 33, 34, and 34A, respectively,for admitting and removing hydrogen and helium to and from the bubblersystem. The system also includes a source of hydrogen 35, a source ofhelium 36, a hydrogen purifier 37, means 38 for admitting a dopant tothe bubbler system, means 39 for admitting nitrogen to the bubblersystem, and variable leak valve 40. The apparatus employed also includesa furnace 41 containing a muffle tube 42 and a quartz reaction tube 43.

In the operation of the growth process, heating of the reaction chamberis initiated, hydrogen from source 35 being diffused throughpalladium-silver membranes in purifier 37 and flowed through controlvalves in the bubbler system to arsenic trichloride reservoir 32.Hydrogen serves as a carrier gas and transports the arsenic trichlorideto reaction chamber 43. Additionally, the hydrogen flow serves as adilute control for the arsenic trichloride flow and for dopant transferto the reaction chamber. Reservoir 32 is maintained at a temperaturewithin the range of 15° C to 25° C during growth, and the flow rate ofhydrogen is maintained within the range of 300 cm³ /min to 400 cm³ /min.

Before initiating the vapor transport process, a source of gallium 44 isintroduced into chamber 43 which also includes a holder 45, on which ismounted a suitable substrate 22, discussed previously in connection withFIG. 2. A solid source of GaAs may alternatively be employed in place ofGa.

The substrate may be tellurium-, selenium-, or silicon-doped n⁺⁺ GaAs,manifesting a resistivity of about 0.003 ohm-cm. These materials arefabricated using techniques well-known to those skilled in the art.

Turning again to the operation of the process, heating of the reactionchamber is continued until the gallium attains a temperature of 760° Cto 810° C and the substrate a temperature of 725° C to 760° C, at whichpoint epitaxial growth is initiated at a rate within the range of 0.05μm/min to 0.3 μm/min. Growth of epitaxial layer 23 of gallium arsenide(FIG. 2) ranging in thickness from 2 μm to 6 μm is continued, thecarrier concentration being maintained at a value within the range of 1× 10¹⁷ cm⁻³ to 1 × 10¹⁸ cm⁻³ by the addition to the reaction system of asuitable dopant, typically sulphur, selenium, and the like, via thevariable leak valve 40. The thickness and carrier concentration ofepitaxial layer 23 are dictated by considerations relating to thedesired resistivity of the deposited layer.

Helium may be used, as taught in U.S. Pat. No. 3,762,945, issued Oct. 2,1973 to J. V. DiLorenzo, to transport additional AsCl₃ to etch eitherthe substrate 22 or the first epitaxial layer 23 in order to obtain asmooth uniform transition between the layers and to prevent theformation of any interfacial layers.

Growth of a second epitaxial layer 24 of gallium arsenide (FIG. 2)ranging in thickness from 4 μm to 8 μm is carried out as above, with thecarrier concentration N_(L) being maintained at a value within the rangeof 1 × 10¹⁵ cm⁻³ to 1 × 10¹⁶ cm⁻³, again introducing a suitable dopantthrough the variable leak valve 40. The thickness and carrierconcentration of epitaxial layer 24 is dictated by considerationsrelating to the desired operating frequency of the finished device, withlower operating frequency associated with greater thickness of layer 24and lower carrier concentration N_(L).

There are a variety of techniques that may be employed where it isdesired to form highly doped regions 28 and 29. For example, forrelatively wide highly doped regions, the variable leak valve 40 may beemployed. Alternatively, at an appropriate time during the growth ofepitaxial layer 24, a known volume of a known concentration of thedopant at a known pressure is instantaneously injected into the reactionchamber. This technique is useful for forming relatively narrow highlydoped regions and is conveniently achieved by using, for example,commercially available 100 ppm to 1000 ppm H₂ S/H₂ as the dopant sourceand a gas injection valve 50. The dopant gas continuously flows at aconstant rate through a tube 51A to exhaust to the atmosphere throughtube 51B. A portion of the tube defines a constant volume region 52between two switching points interior the valve. The carrier gas flowsthrough a second tube 53A to the reaction chamber 43 via tube 53B. Aportion of the second tube may also define a constant volume region 54between two switching points interior the valve. At an appropriate time,both switching points are inverted by handle 55 so that the carrier gassweeps out the dopant gas trapped in the constant volume region 52 intothe reaction chamber. The valve mechanism is surrounded by an inert gas,such as helium, which is introduced via tube 56 and which exhausts tothe atmosphere via tube 57.

From the gas law,

    m = (RT/PV),                                               (2)

where m is the amount of the dopant in moles, R the gas constant, T thetemperature in degrees Kelvin, P the pressure of the dopant gas, and Vthe volume of the dopant gas. By using a known concentration of thedopant (e.g., 1000 ppm H₂ S/H₂) flowing at a known pressure, then thewidths of the highly doped regions 28 and 29 depend only on (1) thegrowth rate of the second epitaxial layer 24 and (2) the volume ofdopant gas injected into the carrier gas stream as determined by theconstant volume region 52. Widths of highly doped regions ranging fromabout 100 Angstroms to 700 Angstroms are easily obtainable by thistechnique. If a portion of the second tube 53 also defines a constantvolume region 54, then repeated switching may be performed to obtain aseries of highly doped regions in the epitaxial layer, withoutinterrupting the growth of the layer.

Use of the technique permits formation of the highly doped regions 28and 29 (FIGS. 2A and 2B). The growth of the second epitaxial layercontinues uninterrupted until a final desired thickness is obtained, toform the lo-hi-lo modified Read structure of FIG. 2B. Alternatively,growth may be stopped after the formation of region 28 to form the hi-lomodified Read structure of FIG. 2A. Other non-uniformly doped structuresmay also be fabricated. The slice is then further processed to fabricatean IMPATT diode by methods well-known in the art, as mentioned earlier.

The foregoing CVD reaction has been described in terms of the Ga/AsCl₃/H₂ disproportionation reaction, where etching of the substrate 22 orfirst epitaxial layer 23 is performed by AsCl₃ carried in helium gas.However, in the case where a solid source of GaAs is employed, such asin the GaAs/AsCl₃ /H₂ disproportionation reaction, there is insufficientchloride (HCl or Cl₂) available for etching. In such a case, theinstantaneous injection technique may be advantageously employed toinject a precisely controlled amount of HCl gas to effect precisionetching. The apparatus shown in FIG. 3 may then include a secondinjection valve at an appropriate location to introduce the HCl throughconduct means 34 to the substrate 22.

EXAMPLE

Square wafers 1 in. on a side were positioned upright in a Ga/AsCl₃ /H₂vapor deposition reactor similar to that shown in FIG. 3. The depositionof the second epitaxial layer was preceded by an in situ etch of theGaAs substrate in AsCl₃ /He and growth of a 4 μm thick n⁺ buffer layer.An 8-port injection valve (Varian Aerograph model 57-000168-00) havingtwo exchangeable sample loops was employed to inject the dopant. Turningthe valve handle 55 by 90° results in an interchange of the contents ofthe two loops 52 and 54. The valve may be operated every few secondswithout loss of doping control.

Typically, H₂ S having a volume of 0.7 ml at a concentration of 300 ppmand 2 atm pressure was injected once, corresponding to n = 1.7 × 10⁻⁸moles and containing 1.0 × 10¹⁶ S atoms. At a growth rate of 0.08μm/min, this amount of H₂ S yielded highly-doped regions 28, and 29,both containing a charge Q of 2 × 10¹² cm⁻².

Typical doping profiles, measured on a conventional capacitance-voltageprofilometer, are shown in FIGS. 4A and 4B. FIG. 4A depicts a hi-lodoping profile. The stop clump has a value of Qs, as determined from theC-V measurement, of 1 × 10¹² cm⁻² and a thickness of about 0.35 μm. FIG.4B depicts a lo-hi-lo profile. The stop clump has Qs of 2 × 10¹² cm⁻²and a thickness of 0.5 μm.

After further processing the slices to fabricate IMPATT diodes from eachslice, the measurements shown in the accompanying Table were obtainedfor the range of breakdown voltage, V_(b) operating frequency, f,microwave efficiency, N, and average d.c. input power at failure.

The Table compares these Read IMPATT diodes with the lo-hi-lo dopingprofile plus a stop clump and two uniformly-doped slices, one having abreakdown voltage of 80 volts and the other a breakdown voltage of 100volts. Control over breakdown voltage, and thus the device operatingfrequency for a uniformly-doped depletion region, is controlled by thedoping alone. Since for the uniform doped IMPATT, f ˜ W⁻¹ (more exactlyW⁻⁰.8) a high voltage resulting from a relatively low doped layernecessarily results in a low frequency device. It is seen in the Tablethat the frequency deviation is less for the lo-hi-lo devices includinga stop clump than for devices without it. This is true even though ingeneral the frequency of non-uniformly doped devices is more difficultto control.

Comparison of frequency control non-uniformly doped depletion regionwith and without stop clump is difficult at this time, since in manyinstances the buffer layer acts as a stop for the depletion layer. Thedistance between the stop clump intentionally added and the buffer layeris too narrow to permit direct comparison. It is expected that adeliberate increase in the epi thickness without the use of the stopclump would result in large variations in both frequency and voltage.

                                      TABLE                                       __________________________________________________________________________                 Operating         Ave D. C.                                               V.sub.B                                                                           Frequency         Input Power                                    Sample                                                                            Profile                                                                            (Volts)                                                                            (GH.sub.z)                                                                         Ave N(%)                                                                            Peak N(%)                                                                           at Failure (Watts)                             __________________________________________________________________________    1   Lo-hi-lo                                                                           78-100                                                                            6.0-5.2                                                                             11.7  17.2   23                                            2   Uniform                                                                             80 ˜7.2                                                                          ˜12                                                                           ˜14                                                                           ˜25                                      3   Uniform                                                                            100 ˜5.5                                                                          ˜12                                                                           ˜14                                                                           ˜25                                      __________________________________________________________________________

What is claimed is:
 1. A process for making a gallium arsenide diodecomprising:a. epitaxially depositing at least one layer of galliumarsenide on the surface of a gallium arsenide substrate from materialsincluding a source of gallium, a source of arsenic, and aconductivity-type determining impurity; b. varying the amount ofconductivity-type determining impurity during the epitaxial depositionin the following sequence:(1) raising the amount of impurity, (2)lowering the amount of impurity, and (3) raising the amount of impuritythis sequence being timed such that a relatively thin region of thelayer, ranging in thickness from 100 Angstroms to 0.5 μm, is depositedwhile the impurity level is raised, so as to form a layer having a firstrelatively thin region formed during step 1 and a second relatively thinregion formed during step 3 both of which regions having an impurityconcentration that is relatively high with respect to the bulk of thelayer, c. forming an electrical contact to the gallium arsenidesubstrate; and d. forming a rectifying barrier contact on the depositedgallium arsenide layer.
 2. The process of claim 1 in which the firstthin region includes an amount of charge ranging from about 1 × 10¹²cm⁻² to 3 × 10¹² cm⁻².
 3. The process of claim 1 in which:(a) two layersof gallium arsenide are epitaxially deposited in sequence on the galliumarsenide substrate from materials including gallium, arsenic trichlorideand sulfur as an n-type determining impurity, the materials beingtransported to the substrate by a carrier gas, the first layer ofgallium arsenide having a carrier concentration of about 1 × 10¹⁷ cm⁻³to 1 × 10¹⁸ cm⁻³ and a thickness of about 2 μm to 6 μm, and the secondlayer of gallium arsenide having a carrier concentration of 1 × 10¹⁵cm⁻³ to 1 × 10¹⁶ cm⁻³ and a thickness ranging from 4 μm to 8 μm; (b) thefirst thin region of gallium arsenide is formed during deposition of thesecond gallium arsenide layer by injecting substantially simultaneouslyat constant pressure a constant volume of a gas containing from 100 ppmto 1000 ppm H₂ S/H₂, the region ranging in thickness from about 100Angstroms to 0.5 μm and including an amount of charge ranging from about1 × 10¹² cm⁻² to 3.5 × 10¹² cm⁻² ; (c) the second thin region of galliumarsenide is formed by injecting substantially instantaneously atconstant pressure a constant volume of a gas containing from 100 ppm to1000 ppm H₂ S/H₂, the thin film ranging in thickness from 0.01 μm to 0.5μm and including a carrier charge ranging from 2 × 10¹² cm⁻² to 3.5 ×10¹² cm⁻² ; (d) forming an ohmic contact on a second surface of thegallium arsenide substrate; and (e) forming a Schottky barrier contacton the second gallium arsenide layer.
 4. The process of claim 1 in whichthe sequence through which the amount of conductivity-type determiningimpurity is varied includes the additional step of 4) lowering theamount of impurity, so that the two thin regions are bounded on bothsides by regions of the layer with relatively lower concentration ofimpurity.
 5. The process of claim 4 in which the first thin regionincludes an amount of charge ranging from about 1 × 10¹² cm⁻² to 3 ×10¹² cm⁻².
 6. The process of claim 4 in which:(a) two layers of galliumarsenide are epitaxially deposited in sequence on the gallium arsenidesubstrate from materials including gallium, arsenic trichloride andsulfur as an n-type determining impurity, the materials beingtransported to the substrate by a carrier gas, the first layer ofgallium arsenide having a carrier concentration of about 1 × 10¹⁷ cm⁻³to 1 × 10¹⁸ cm⁻³ and a thickness of about 2 μm to 6 μm, and the secondlayer of gallium arsenide having a carrier concentration of 1 × 10¹⁵cm⁻³ to 1 × 10¹⁶ cm⁻³ and a thickness ranging from 4 μm to 8 μm; (b) thefirst thin region of gallium arsenide is formed during deposition of thesecond gallium arsenide layer by injecting substantially simultaneouslyat constant pressure a constant volume of a gas containing from 100 ppmto 1000 ppm H₂ S/H₂, the region ranging in thickness from about 100Angstroms to 0.5 μm and including an amount of charge ranging from about1 × 10¹² cm⁻² to 3.5 × 10¹² cm⁻² ; (c) the second thin region of galliumarsenide is formed by injecting substantially instantaneously atconstant pressure a constant volume of a gas containing from 100 ppm to1000 ppm H₂ S/H₂, the thin film ranging in thickness from 0.01 μm to 0.5μm and including a carrier charge ranging from 2 × 10¹² cm⁻² to 3.5 ×10¹² cm⁻² ; (d) forming an ohmic contact on a second surface of thegallium arsenide substrate; and (e) forming a Schottky barrier contacton the second gallium arsenide layer.